Bring water to a boil in a medium saucepan; stir in groats. Bring mixture to a boil; cover, reduce heat, and simmer 24 to 26 minutes or just until tender.
Combine groats, cucumber, and next 8 ingredients in a bowl; set aside.
Drain groats and rinse under cold water. Drain well, and add to cucumber mixture. Cover and chill 3 hours.
Add feta cheese; toss gently before serving.